Question

Two blocks, each with a mass of 15.0 kg, are placed on a frictionless horizontal surface and are connected by a massless spring with a spring constant of k = 190 N/m. If you apply a horizontal force of 20.0 N to one of the blocks, then how much will the spring compress as the boxes accelerate?

Answer 1

By applying Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement, we find that a spring with a constant of 190 N/m compresses by approximately 0.10526 m or 10.526 cm when a 20.0 N force is applied on a frictionless surface.

Step-by-step explanation:

To solve how much the spring will compress due to the applied force, we first recognize this as a physics problem involving Hooke's Law, which states that the force exerted by a spring is proportional to its displacement (x) from its equilibrium position, mathematically described as F = -kx, where k is the spring constant. The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement.

We can set up the equation with the known force and spring constant:

• F = kx
• 20.0 N = (190 N/m)x
• x = 20.0 N / 190 N/m
• x = 0.10526 m

The spring compresses by approximately 0.10526 meters or 10.526 centimeters when the 20.0 N force is applied. It's important to note that since the surface is frictionless and the spring is massless, we only consider the force applied and the spring constant in our calculation.